SOLUTION : $\quad a^* b=\text { l.c.m. of } a \text { and } b $
$\therefore \quad 2{ }^* 3=\text { I.c.m. of } 2 \text { and } 3 $
$\quad=6$
${[\because \text { l.c.m. of } 2 \text { and } 3=2 \times 3=6]}$
$\text { By } \quad 6 \notin\{1,2,3,4,5\}$
$\text { Hence * is not a binary operation on }\{1,2,3,4, 5\}$